Integers are sets of whole numbers that include positive, negative, and zero numbers and are commonly represented by the ‘Zahlen’ symbol Z=…, -4, -3, -2, -1,0,1,2,3, 4… It’s worth noting that an integer can’t be a fraction, decimal, or percentage. Whole numbers, on the other hand, are a set of positive and zero numbers that do not contain a decimal point or fractions. Whole numbers are written as W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,………….
It should be noted that while all whole numbers are integers, not all integers are whole numbers, based on the definitions above. Integers are made up of negative, positive, and zero digits, while whole numbers are made up of only positive and zero digits. As a result, integers produce entire numbers.
Integers are Divided into three Categories:
- Negative Numbers
- Positive Numbers
- The number 0
Whole numbers with a plus sign (+) in front of the numerical value are known as positive numbers. In most cases, the plus sign is omitted and the symbol is simply represented without it. Positive numbers, as well as zero, are greater than negative numbers. On the number line, positive numbers are usually showcased from the right side of zero. 2, 88, 800, 9900, and so on are examples of positive numbers.
A dash or minus sign in front of a numerical value represents a negative number. On the number line to the left of origin, these numbers are represented. Negative numbers include…, – 800, –100, -10, -2, and -1.
On the number line, zero stands on a neutral ground. It has neither a positive nor a negative connotation. Hence it is a null number.
Whole numbers have a variety of properties. These properties are dependent on addition, subtraction, division, and multiplication.
The sum of two whole numbers, for example, is always a whole. Subtraction of two whole numbers, on the other hand, may result in a whole number of an integer. When two whole numbers are multiplied, the product is a whole number. On the other hand, division may not produce a fraction or a whole amount.
Instructions for Signed Integer Values:
Signed Integer Numbers Addition
Subtract the absolute values by adding two integers with different signs, and write down the difference with the symbol of the number with the highest absolute value. (-4) + (+2) = -2 (+6) + (-4) = +2, for example.
Subtraction of Signed Integers
Adjust the sign of the second number being subtracted and obey the addition rules when subtracting two integers.
For instance, (-7) – (+4) = -7 -4 = -11
Division and Multiplication of Signed Integer Numbers
The law for multiplying and dividing two integer numbers is straightforward. The result is positive if both integers have the same symbol. If the signs of the integers vary, the result is negative. (+2) x (+3) = +6 and (+3) x (-4) = – 12 is an example.
Likewise, (+6)/(+2) = +3 and (-16)/ (+4) = -4.
Applications of Integers:
Integers are more than just numbers on a piece of paper; they have a wide range of practical applications. In the real world, positive and negative numbers have different effects. They’re often used to represent two opposing circumstances. Positive numbers are used to mean temperature when it is above zero, while negative numbers indicate temperature when it is below zero. They allow you to compare and calculate two things, such as how large or small something is, or how many more or less things there are, and thus quantify things. Players’ scores in baseball, football, and hockey competitions, movie or song ratings, and bank credits and debits are interpreted as positive and negative numbers, respectively, are examples of real-life cases where integers are used. Whole numbers and integers are commonly used in a variety of fields. Whole numbers, for example, are used to describe the population of a set of quantities. Since the population cannot be negative, whole numbers are used. In banking, integers are used to indicate whether a transaction is debit or credit. Integers are often used to characterise a body’s temperature, which may be below or above zero degrees Celsius. In sports, integers are used to indicate goal disparities.